Analogy between equilibrium beach profiles and closed universes

TL;DR

This paper draws an analogy between equilibrium beach profiles and closed universe models in cosmology, using variational principles and cosmological equations to analyze and clarify properties of beach profiles.

Contribution

It reformulates the beach profile problem using cosmological equations, providing new insights and resolving controversies through an interdisciplinary approach.

Findings

Analytic solutions for beach profiles derived from cosmological equations

Qualitative properties of beach profiles clarified using cosmological analogy

Resolution of existing controversies in beach profile analysis

Abstract

We reformulate the variational problem describing equilibrium beach profiles in the thermodynamic approach of Jenkins and Inman. A first integral of the resulting Euler-Lagrange equation coincides formally with the Friedmann equation ruling closed universes in relativistic cosmology, leading to a useful analogy. Using the machinery of Friedmann-Lema\^{\i}tre-Robertson-Walker cosmology, qualitative properties and analytic solutions of beach profiles, which are the subject of a controversy, are elucidated.